Question
If α, β, γ are the roots of the equation x3+4x+1=0,then (α+β)−1+(β+γ)−1+(γ+α)−1=
Answer: Option C
:
C
If α,β,γ are the roots of the equation
α+β+γ=0,αβ+βγ+γα=4,αβγ=−1
therefore(α+β)−1+(β+γ)−1+(γ+α)−1
=1−γ+1−α+1−β
=−(αβ+βγ+γααβγ)
=−(4−1)=4
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:
C
If α,β,γ are the roots of the equation
α+β+γ=0,αβ+βγ+γα=4,αβγ=−1
therefore(α+β)−1+(β+γ)−1+(γ+α)−1
=1−γ+1−α+1−β
=−(αβ+βγ+γααβγ)
=−(4−1)=4
Was this answer helpful ?
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